Saturday, 7 July 2012

Cutting up Space, Part 2: The Laws of Form

G.
Spencer Brown's fabulous book on the calculus of indications, The
Laws of Form,
begins thus:

The
theme of this book is that a universe comes into being when a space
is severed or taken apart. The skin of a living organism cuts off an
inside from an outside. So does the circumference of a circle in a
plane. By tracing the way we represent such a severance, we can begin
to reconstruct, with an accuracy and coverage that appear almost
uncanny, the basic forms underlying linguistic, mathematical,
physical, and biological science, and can begin to see how the
familiar laws of our own experience follow inexorably from the
original act of severance.

Who
would not want to continue reading this book after that enticingly
fabulous introduction? Especially someone like myself who is
interested in both language and urban space (specifically
psychogeography and poststructuralist theory).

While
the above paragraph sounds very philosophical, the book is
nevertheless a mathematics-based book also, which includes Boolean
algebra, the algebra of logic. This mostly appears in the form of
symbols and simple formula, most of which is beyond me. However, I do
understand the philosophical material, al lot of which is redolent of
non-dual eastern philosophical discussion - and indeed G. Spencer
Brown was a student of R. D. Laing (many of the terms Brown uses are
translatable into psychoanalysis: for example, condensation and
compensation). The concepts can also be applied to theories of self and
other, of which Laing has written.

The
book was described in its day as a mathematics of consciousness and
became useful as a springboard into the theory of autopoiesis
(Maturana and Varela) and in second-order observation.

It
is a mark that forms a boundary, separating one space from another by
creating a distinction. An inside and an outside, or a 'this' and
everything else that isn't 'this, if you will. It also assumes an
observer of the differentiation. Various actions can then be taken
that involve crossing the boundary - once or twice, crossing then
returning, etc. - and the result of carrying out these transactions.
This mark, the cross, when it exists creates a marked state. When it
does not it is an unmarked state, or the void, or nothingness (hence
it's relationship to non-dual Eastern religion).Already
you may be able to see the potential relationship with deconstruction
and its interest in the binary oppositions inherent in language. Not
as much as you might expect has been written about the relationship
between the two, although Niklas Luhman has done so, since he is a
proponent of second-order observation theory too. There is also some
parergonal logic in the Brown text. As discusses by Jacques Derrida
in The
Truth in Painting (in
very simple terms, where the framing of the artwork creates both a
division but also a bridge, this concept also being applied to theory
itself).My
potential interest in the book in relationship to its uses in
psychogeography are around the ideas of inclusion/exclusion,
directions of observation, urban planning and zoning, crossing
boundaries, self and 'the other', etc. I'd be interested in any
mathematical psychogeographers who might have some more thoughts
about it.

I'll
sign off with this brilliant passage from the notes at the end of the
book:

[In
order for the universe to have the function of seeing itself]
evidently it must first cut itself up into at least one state which
sees, and at least one other state which can be seen. In this severed
and mutilated condition, whatever it sees is only partially itself. We may take it that the world undoubtedly is itself (i.e. is
indistinct form itself), but, in any attempt to see itself as an
object, it must, equally undoubtedly, act so as to make itself
distinct from, and therefore false too, itself. In this condition it
will always partly elude itself.

NB: I have a beautiful second edition copy of the book. I had wanted a copy for a long time so treated myself to one for completing my Masters. It has a great 1970s-esque cover, shown below:

2 comments:

Very interesting. It reminded me of Thompson's wierd incorporation of geometry in his anthropology of waste: Rubbish Theory (1979) and also of Douglas' (1966) Purity and Danger, specifically her masterful examination of the role of parsing the world in the making meaning of it.